ORNSTEIN-ZERNIKE-LIKE EQUATIONS IN STATISTICAL GEOMETRY - STABLE AND METASTABLE SYSTEMS

Statistical geometric methods based on nearest-neighbor distributions are used, in connection with hard-particle systems, to develop Ornstei n-Zernlike-like equations that have already been of considerable value in the statistical thermodynamic analysis of such systems and that pr omise to have even greater value. In this paper, we use these equation s to (1) develop a relation that is valid for a hard particle system i n unconstrained equilibrium and that shows that the insertion probabil ity cannot vanish (short of closepacking) in such a system, (2) study the still incompletely settled issue concerning the equality of the ha rd-particle densities on the peripheries of cavities which are and are not occupied by hard particles and, in so doing, arrive at a relation that holds in a system in stable equilibrium but fails in a metastabl e system, (3) provide insight into the geometric mechanism of hard-par ticle phase transitions and allow simple estimates of the freezing den sities, and (4) suggest a new physical interpretation for the direct c orrelation function.